In 1580, just after publishing the first edition of his Essays, Montaigne had an audience with Henri III in Paris. Henri said he liked the book very much, to which Montaigne reportedly replied, "Sir, then your majesty must like me". For, as he always maintained, he and his essays were one. "I have no more made my book than my book has made me", he wrote, "it is a book consubstantial with its author".

And this was just the beginning. By the time of its publication, he and his text had been growing together for eight years; now he would add material for 12 more, probably until the year of his death, 1592. More editions came out, and he left annotated copies for a vast posthumous one. He seems to have amazed even himself: "Who does not see that I have taken a road along which I shall go, without stopping and without effort, as long as there is ink and paper in the world?"

All this writing and tinkering rarely took the form of changing anything, or crossing out old versions. When Montaigne thought of some new angle on a question, he usually inserted it without further adjustment, even if this produced contradictions. He preferred not to repent of choices he had made either in literature or in life. His past selves each had their own voice, even if the new Montaigne no longer understood them. Thus, within a paragraph or two of the Essays, we may meet Montaigne as a young man, then as an old man with one foot in the grave, and then again as a middle-aged mayor bowed down by responsibilities. We may listen to him complaining of impotence; a moment later we see him young and lusty and bent on seduction. "I do not portray being", he wrote; "I portray passing. Not the passing from one age to another … but from day to day, from minute to minute." His let his thoughts lie where they fell.

Why did he do it? What, really, was he trying to achieve by "essaying" his life for so long? His love of communication had something to do with it. But writing also helped him to live a better life: to become more truly, and more thoughtfully, himself.

Thus, he wondered, "if no one reads me, have I wasted my time?" No: for, just as he had formed the book, so writing the book had helped to form his own personality. Writing made him live differently. "In modeling this figure upon myself, I have had to fashion and compose myself so often to bring myself out, that the model itself has to some extent grown firm and taken shape." It made him take more care over life, and pay more attention. Others looked ahead; he looked within. "I continually observe myself, I take stock of myself, I taste myself … I roll about in myself."

The idea of cultivating full awareness of every instant owed much to the Stoic and Epicurean philosophers of antiquity. One of Montaigne's favourites, Seneca, wrote that life runs through our fingers like water. We cannot stem the flow, but we can drink deeply while it is there. Philosophy helps to remind us to do this. It works like the mynah birds in Aldous Huxley's novel Island, which are trained to fly around all day calling "Attention! Attention!" and "Here and now!" The pages of Montaigne's book were his mynah birds. So determined was he to squeeze out every drop of his life's experience that he had a long-suffering servant wake him repeatedly in the middle of the night, so he could catch a glimpse of his own sleep as it left him. No wonder the 20th-century philosopher Maurice Merleau-Ponty described Montaigne as someone who put "a consciousness astonished at itself at the core of human existence".

Montaigne liked to say that the Essays were a casual pursuit, thrown on paper in idle hours. But at times he confessed to the difficulties of this discipline of attention and astonishment. "It is a thorny undertaking, and more so than it seems, to follow a movement so wandering as that of our mind, to penetrate the opaque depths of its innermost folds."

As he got older and realised that the life remaining to him could not be of great length, he exerted himself even more. "I try to increase it in weight," he wrote, "I try to arrest the speed of its flight by the speed with which I grasp it ... The shorter my possession of life, the deeper and fuller I must make it." At every moment, he brought himself back to himself. "When I walk alone in the beautiful orchard, if my thoughts have been dwelling on extraneous incidents for some part of the time, for some other part I bring them back to the walk, to the orchard, to the sweetness of this solitude, and to me."

The result was an almost Zen-like presence of mind in the moment. It sounds simple, but nothing is more difficult. This is why Zen masters spend a lifetime, or several lifetimes, learning the art of it. Even then, according to traditional stories, they need a teacher to keep rapping them with a long stick - the keisaku, designed to remind meditators to remain mindful. If Montaigne achieved even a fraction of this after one, fairly short lifetime, perhaps it was because he spent so much of that lifetime scribbling on paper with a very small stick.

Montaigne's motivation is an ancient one: in the attempt to live well, he reached back to the oldest of western philosophies. Yet his fascination with the flow of experience seems modern: it foreshadows our own relentless self-documentation in images, words and video clips. Are we too self-absorbed already? Are we all Montaignes now? Is he good or bad for us? Can writing (and reading) make us wise? These will be our questions for next week.